Residual Plots

The MIXED procedure can generate panels of residual diagnostics. Each panel consists of a plot of residuals versus predicted
values, a histogram with normal density overlaid, a Q-Q plot, and summary residual and fit statistics (Figure 65.15). The plots are produced even if the OUTP=
and OUTPM=
options in the MODEL
statement are not specified. Residual panels can be generated for marginal and conditional raw, studentized, and Pearson
residuals as well as for scaled residuals (see the section Residual Diagnostics).

The graphs are created when ODS Graphics is enabled. The panel of the studentized marginal residuals is shown in Figure 65.15, and the panel of the studentized conditional residuals is shown in Figure 65.16.

Figure 65.15: Panel of the Studentized (Marginal) Residuals

Since the fixed-effects part of the model comprises only an intercept and the gender effect, the marginal mean takes on only
two values, one for each gender. The "Residual Statistics" inset in the lower-right corner provides descriptive statistics
for the set of residuals that is displayed. Note that residuals in a mixed model do not necessarily sum to zero, even if the
model contains an intercept.

Figure 65.16: Panel of the Conditional Studentized Residuals

Influence Plots

The graphical features of the MIXED procedure enable you to generate plots of influence diagnostics and of deletion estimates.
The type and number of plots produced depend on your modifiers of the INFLUENCE
option in the MODEL
statement and on the PLOTS=
option in the PROC MIXED
statement. Plots related to covariance parameters are produced only when diagnostics are computed by iterative methods (ITER=
). The estimates of the fixed effects—and covariance parameters when updates are iterative—are plotted when you specify the
ESTIMATES
modifier or when you request PLOTS=
INFLUENCEESTPLOT.

Two basic types of influence panels are shown in Figure 65.17 and Figure 65.18. The diagnostics panel shows Cook’s D and CovRatio statistics for the fixed effects and the covariance parameters. For the SAS statements that produce these influence
panels, see Example 65.8. In this example, the impact of subjects (Person) on the analysis is assessed. The Cook’s D statistic measures a subject’s impact on the estimates, and the CovRatio statistic measures a subject’s impact on the precision
of the estimates. Separate statistics are computed for the fixed effects and the covariance parameters. The CovRatio statistic
has a threshold of 1.0. Values larger than 1.0 indicate that precision of the estimates is lost by exclusion of the observations
in question. Values smaller than 1.0 indicate that precision is gained by exclusion of the observations from the analysis.
For example, it is evident from Figure 65.17 that person 20 has considerable impact on the covariance parameter estimates and moderate influence on the fixed-effects
estimates. Furthermore, exclusion of this subject from the analysis increases the precision of the covariance parameters,
whereas the effect on the precision of the fixed effects is minor.

Figure 65.18 shows another type of influence plot, a panel of the deletion estimates. Each plot within the panel corresponds to one of
the model parameters. A reference line is drawn at the estimate based on the full data.